A few considerations are in order. First of all, we observe that in the Landau gauge a separate mass term for the trace of \(A_{\mu \nu }(x)\)  is forbidden, in close analogy to what happens in massive LG [1]}. Moreover, having introduced a mass term, we have the new propagator (REF ) with coefficients (REF )-(), which we would like not to have tachyonic poles [2]}. With our choice of the metric \(\eta _{\mu \nu }=\mbox{diag}(-1,1,1,1)\)  we need that the coefficient of \(p^2\)  and the mass term have the same sign, and this identifies two allowed regions in the \((a,m_1)\) -plane.
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